关于微分同胚的一个充分必要条件(英文)

A Necessary and Sufficient Condition on Diffeomorphisms

英文关键词:C^r-dffeomorphism  adjoint equivalence  inherent W.G.-sheaf.

中文摘要:

      确定两个流形是否C^r-微分同胚是微分流形研究中的重要课题，本文定义了反层的概念，给出了反层范畴，由此找到两个微分流形，C^r-微分同胚的特征刻画，于是给出了一种较以往更优的判定法．

英文摘要:

      We introduce anti-sheaves for C^r-manifolds and a category of anti-sheaves. The adjoint equivalence between the category of anti-sheaves and the category of C^r-manifolds is established. Using such an equivalence, we obtain a characterization for deciding whether two given manifolds arc C^r-diffeomorphic in terms of inherent W.(G)- sheaves. This provides the first known criterion for determining whether two given man- ifolds are diffeomorphic.